I've always used a follower on my first 4 characters, but there have been times I wished I hadn't because they get in the way, sometimes.
A few weeks ago, I started another character - permanent level 1 - who cannot level up.
Although I did get the quest to talk to the Jarl about Helgen/Riverwood, I have not done that, and as a result don't have a follower yet (nor the house in Whiterun, which really causes problems storing stuff).
I cannot carry as much, and often use the warmaiden's shop to dump stuff on the floor while I go dungeon crawling. And playing solo forces me to become more aware of my surroundings - always have to be ready to fight, lots of wolves and thiefs out there.
But I like it, only have to worry about myself - which takes me back to my FPS days - and not about trying to keep a follower alive.